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Analytic Solution to Mild Slope Equation for Transformation of Waves Propagating over an Axi-symmetric Pit  

Jung, Tae-Hwa (School of Civil, Urban and Geosystem Engineering, Seoul National University)
Suh, Kyung-Duck (School of Civil, Urban and Geosystem Engineering & Engineering Research Institute, Seoul National University)
Publication Information
Journal of Korean Society of Coastal and Ocean Engineers / v.18, no.4, 2006 , pp. 308-320 More about this Journal
Abstract
An analytic solution to the mild-slope equation is derived for waves propagating over an axi-symmetric pit. The water depth inside the pit varies in proportion to a power of radial distance from the pit center. The governing equation is transformed into ordinary differential equations by using separation of variables, and the coefficients of the equations are transformed into explicit forms by using Hunt's (1979) approximate solution. Finally, by using the Frobenius series, the analytic solution is derived. Due to the feature of Hunt's equation, the present analytic solution is accurate in shallow and deep waters, while it is less accurate in intermediate depth water. The validity of the analytic solution is demonstrated by comparison with numerical solutions. The analytic solution is also used to examine the effects of pit geometry and relative depth on wave transformation.
Keywords
pit; analytic solution; mild slope equation; wave transformation;
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